Posted
by
Soulskill
on Monday April 11, 2011 @06:34PM
from the is-it-pointless-to-play-drug-wars-while-looking-productive dept.

An anonymous reader writes "Texas Instruments and Casio have recently released new flagship graphical calculators but what, exactly, is the point of using them? They are slow, with limited memory and a 'high-resolution' display that is no such thing. For $100 more than the NSpire CX CAS you could buy a netbook and fill it with cutting edge mathematical software such as Octave, Scilab, SAGE and so on. You could also use it for web browsing, email and a thousand other things. One argument heard for using these calculators is: 'They are limited enough to use in exams.' Sounds sensible, but it raises the question: 'Why are we teaching a generation of students to use crippled technology?'"

Why are we teaching a generation of students to use crippled technology?

Cause the large portion of students are untrustable cheating bastards? Ok, a little bit of hyperbole, but that really is the reason. In addition to web browsing, you could also load equation solvers and all manner of tools to enable one to cheat their way through math. The old way overpriced graphing calculators can be wiped before a test, and offer the right mixture of functionality and cripple that schools want.

The price I think is just a function of having a captive consumer base. They charge as much for something that should cost so very little because the people who need it are going to buy it.

And yes, I'm sure the ol` "in real life I'd google the answer anyway" point is going to come up, and while I agree for most traditional memorize and regurgitate type courses, I still think math should be tough with a reasonable distance from crutches, while at the same time not trying to pretend they don't exist either. Show them matlab, but make `em work it out on paper on the test.

The thing is, even the "standard" graphing calculators are now advanced enough to teach with. Smart teachers are now demanding students reformat their calculators before a test, because otherwise they (like me) would just write a BASIC program instead of memorizing a formula, or store notes as an image.

Of course, I wrote a BASIC program that mimicked the shell, except a) it did not actually reformat, just display a message that it did so, and b) like a rootkit, it displayed false values for stored data, in this case blanks. It wasn't flawless (the ON key would interrupt the program), but none of my teachers figured it out. Arguably, it was more work than memorizing the formulas in the first place. Also arguably, this was more useful to me than rote-learning the proof of the quadratic formula.

Also arguably, this was more useful to me than rote-learning the proof of the quadratic formula.

I would like to hear that argument.

I've had a student argue that the skills involved in plagiarizing a paper about Nabokov's Pale Fire were more valuable than reading the great novel and doing the thinking and writing involved in producing an original paper. I wonder why some 20 years old would think he had the merest grasp of what would or would not be "useful" to him.''

After all, learning to braze or cadweld a pipe could be much more useful than learning to solve a partial differential equation, if you wanted to be a plumber.

Looking back on my own education, the one quality I wish I'd had more of is humility.

Because writing a fairly complicated program with the described functionality requires all of the skills, and more, involved in the proof of the quadratic formula (which is an especially trivial proof if you already know the formula). It's objectively more useful to learn, because it requires the same skills and other skills as well, not just differently useful (requiring different skills of unrelated application).

I learnt a salutory lesson in high school back in the 1980s. Our maths teacher had given us dozens of simple functions and told us to graph them in polar coordinates. the first couple took me ages, calculating and plotting each point by hand. I felt comfortable that I knew how polar coordinates worked and felt I had no need to do each example in the problem set. So I wrote a simple BASIC program to do all the rest for me. I didn't bother to hide the fact, and handed in the results on dot matrix paper. My teacher queried it, and I explained that being able to write a programme to plot functions in polar coordinates proved that I understood the work. So he asked me what patterns I'd noticed. Off the top of my head, what would such-and-such a function look like? It was only then that I realised that in writing my programme, I hadn't just saved myself a lot of rote work, I'd skipped a lesson designed to force me to puzzle out the patterns. (Fortunately, it was a fairly simple set of patterns and it only took a moment's thought before I could answer the question, but if he hadn't asked, I might never have noticed and might have been reduced to plotting these things out one point at a time when exam time came).

With THIS you have grasped what many people just fail to see. Intuition should become part of every learning in life. I have a friend who has gotten nothing but high distinctions throughout her entire engineering degree. She is a mathematical genius. You drop a circuit in front of her she can solve all the steady state values in a minute, she can also quickly give you any gain or AC analysis.

But she can't grasp what a circuit does. If you put a drawing of an amplifier with some reactive components in the feedback loop in front of her she can't simply come out and say low pass or high pass. Put a powersupply circuit and she won't within a second answer if it's a buck or boost, if the capacitor is used to smooth output ripple, etc.

People miss this fundamental learning in all degrees. So you know how to write a quick sort, good for you, so do I with 2seconds of googling. But do you know when to use the quicksort on a dataset instantly and intuitively without googling for "What is the best sorting algorithm?"

Details can always be worked out or looked up. Conceptual vision and intuition however are the lifeblood of most professions, and people often miss this part about rote learning.

I've had a student argue that the skills involved in plagiarizing a paper about Nabokov's Pale Fire were more valuable than reading the great novel and doing the thinking and writing involved in producing an original paper.

Wow, it would have been at least marginally clever if he'd claimed Zemblan diplomatic immunity...

One might point your student to Laughter in the Dark: you know, the Nabokov novel about the dilettante who's self-satisfaction and self-deception are his undoing.

I wrote what was practically an entire operating system in a VERY limited version of BASIC. That took (if I do say so myself) a remarkable amount of programming skill. Some of the things I first did there (subroutines, nested loops, text parsing) are now things I use daily (GOTO, thankfully, not being one of them).

Meanwhile, I have not used the quadratic formula since I finished Calculus, let alone had to recite a proof of it. I have little doubt that knowing what the formula is and how to use it is relatively important. However, I would like to see a plausible theoretical situation in which one would need to recite a proof of the quadratic formula, without the use of any references.

Meanwhile, I have not used the quadratic formula since I finished Calculus, let alone had to recite a proof of it. I have little doubt that knowing what the formula is and how to use it is relatively important. However, I would like to see a plausible theoretical situation in which one would need to recite a proof of the quadratic formula, without the use of any references.

There are a lot of posts like this, so apologies for singling you out... But, as a math teacher I have to say in response to the "but I never use this" ideas...

Though doing such things is required as class, mathematics is NOT and has never been about memorizing formulas, or even about using specific ones. Yes, we all know you probably don't use the quadratic formula in real life, nor to you have to find the rules for number sequences, nor do you have to find all of the number patterns you can in Pascal's triangle, nor do you have to use Pascal's triangle as a convenient shortcut for binomial expansions, nor do you have to do proofs using all of those uselessly memorized names and properties from your various classes, etc. Yes, you probably had to do all of these things and more in your math classes, but believe it or not, learning math is not really about these things.

Mathematics is (or should be) the class where you learn how to think logically, and use logical and critical thinking skills to solve problems. Not just math problems, but ANY kind of problem you are likely to encounter in life. No, you won't ever use pythagorean theorem to solve relationship problems in your love life, but the logical and critical thinking styles you gained in your mind from solving problems in math will apply to you finding reasonable and logical solutions in real life.

Not only are you learning how to think in math, but you are learning how to break down your thinking so you can check it step by step to make sure there are no flaws. THAT is why we math teachers make you show your work. I, for one, don't care if you get the correct answer or not. I care about how you arrived at your answer, if you can show me the process you used to get to it, and if, in the case of an incorrect answer, you can find the flaw in your thought process that lead to your mistake. Tell me the ability to explain your thinking or the process you intend to engage in to reach a particular outcome is not an important and necessary life skill!

The fact that we use mathematics to try to teach these things is a side effect of what math is. But math class is not just for learning math. It is the class where you exercise your brain so that logical thinking and sustained reasoning become easier in all aspects of life.

And that is why learning to prove the quadratic formula, rather than programming the answer into your calculator, is important.

Mathematics is (or should be) the class where you learn how to think logically, and use logical and critical thinking skills to solve problems. Not just math problems, but ANY kind of problem you are likely to encounter in life"

But it's not taught that way.

It's never taught that way in US schools. Ever. It's always taught as an abstraction without ever tying any of it to real life. Ever. (repetition for emphasis) So when students complain about not ever being able to use this stuff in real life, maybe y

It's never about critical thinking. It's never about solving real life problems. It's always about passing the next test or quiz.

And, again, you miss the point. I apologize if I didn't make that clear. It's not about directly solving real life problems. It's about learning the STYLE AND WAY OF THINKING LOGICALLY in order to solve real life problems.

The way math classes make you do this is by doing math problems, because math problems can only be solved by logical thinking and a logical application of mathematical properties. Doing this again and again, building in complexity over the years, doesn't just teach you to solve math problems, it teaches you HOW TO THINK about any problem. Just like muscular exercise builds up muscles that are used repetitively for some task that you want to be stronger at doing, the kinds of problems you do in math are brain exercises that build up, through repetitive use, the pathways that are useful for logical thinking.

I'm sorry if your teachers didn't make this explicitly clear to you. A lot of teachers don't. I, for one, do explain this to my students, because I understand very well that the level of math we are doing is not very interesting, the types of problems we solve with it are very contrived and not realistic (because the math required to solve "real" problems is way beyond these basics, but you must master the basics if you want to learn to do the advanced stuff), and a lot of the actual things we do in class are not very applicable themselves in real life. For most people, math is not exciting or interesting. But learning it gives the gifts of clear and logical thinking and the ability for sustained chains of reasoning.

I'm sure not many of my students get this, even though I have explained it to them, but that's simply a product of them being young and inexperienced with the world. If even a few of them come out of this class as clearer, more rational thinkers, then I've done my job well.

"...mathematics is NOT and has never been about memorizing formulas.... Mathematics is (or should be) the class where you learn how to think logically, and use logical and critical thinking skills to solve problems."

Bingo! When we learn to read, we begin with simple phonetics with simple words ("See Spot run"), then we are taken though a series of increasingly difficult texts. None of these texts are directly useful later in life. It's the same with math - you start out with basic operations, and move on

It's not the logic of solving problems you should be teaching. Anyone can do that, easily, with or without math. We call them arts grads. It's the quantitative analysis that's important. Ok so you aren't using the quadratic formula in your love life. It's the wrong tool. A statistical analysis of activities engaged in, money invested, the probability of loss due to breakup etc. are all very legitimate mathematical tools in to assess the risk/rewards involved in any relationship. Moreover you need to be confident in the validity of the tools you use to solve a problem. Take something simple, like choosing the specific shade of blue in the google logo, or the background on your corporate letterhead. Now, you can use a 'logical' approach, and feel good about appropriate contrast or the 'tone' the colour conveys. Or you can use survey people (how many is significant?), quantize the various options (how do you quantize them?), and view it as an optimization problem to pick the the optimal colour for the problem you are solving. The latter is the correct (if somewhat expensive) way to choose, the former is what you have arts majors for. If you are a 5 person company, the arts major approach is all fine and good. If you are nokia, google or IBM you damn well better have some actual analysis behind your choice of what font to use, what colour to use etc. because even subtle variations effect perception of your brand, and when you're a company worth 10's of billions of dollars, fractional percent shifts in the value of your brand equate to millions of dollars.

Most of what we learned in math, that seemed basically useless to everyone who wasn't going to be an engineer or a physicist (I was originally a physicist), ended up 15 years later hitting me in the head as a game developer. Quantitatively defining fun, defining the world all of those things are both mathy, and require a lot formal proofs of either correctness or at least derivations of whatever it is you're trying to solve. Computers simulate the world through math, and mathematical approximation, so by extension any field which requires computer models necessarily relies on math to build those tools accurately. The better you are at math, the better the models will be. If you want them to be fast, have good cache hit ratios, minimize memory use, etc. then you can come to a computer scientist. I note that I'm really a developer, not a designer. The designers come up with all these ideas on what would be fun, and I have to find a way to analytically assess them. Is this UI placement better or worse than that one? Is this area too hard or too easy? Solving those problems regularly requires derivations and proofs, and the developers have to come up with them themselves (they aren't just in a book somewhere I can look up), well ok, some tools are in books. But most of them are situational at best.

Do I use the quadratic formula? Not so much at the moment. Do I use its proof and derivation on a regular basis, absolutely. I'm working with a hex grid pathfinding algorithm, and I work with some curvalinear coordinate systems (not all of which are your standard spherical or cylindrical) to attach visual effects to various things. Not far off from where I thought I'd be 15 years ago (hex grids were all the rage in the 90's wargaming scene).

Applying numbers to real problems, either for simulator or for actual analysis, whether its' physical simulation or finance or the like, developing and understanding what your toolkit is, how to use it, and where it will fail is the point of teaching math. If your goal is a 'logical approach to problem solving' you're either on a course for people who won't ever be capable of using math to solve problems, or you're doing it wrong. How do you quantize it, how do you analyse it, how do you prove that your answer is optimal, or if it is intractably hard to optimize it, how efficient is it, and what approximations did you take to get here?

I would argue mathematical analysis is the only way to to provide insight about the world. Everything else is philosophy. If you can replace any philosophical theory with scientifically verifiable one, which is by definition based on math, you have obsoleted the philosophical theory with a better one. If you can't replace a philosophical theory (for example one related to politics or law and justice) with science then you are still better with a mathematical analysis of the problem which may be economic i

Exactly. For proof of this, just look at who runs our society: politicians. They're all a bunch of liars and cheats. Do they ever get in trouble for it? No. Usually, they retire in luxury, and at the very worst, they get caught in a scandal and are forced to resign, but you never see those guys on a street corner begging for food.

Probably because when you're 20 years old you know what you want to do in life

If this was the case, then this student was a fool. This is the twenty-first century, where everyone has three careers and most people have a midlife crisis where they reevaluate their objectives and realize they wish they'd paid more attention in their liberal arts classes.

If I ask you to write a paper on a specific book, but you decide to turn in a creative essay because "it is more valuable of an exercise", I'm going to grade you on how well you accomplished writing a paper for that book. If you really care about "the learning value of the assignment", then I can laugh when you whine about the grade

This is the sort of typical lazy anti-intellectualism that Americans seem to cherish. Only in America can you decide you don't need the lessons in a book without going to the t

I and many of my professors were of the opinion that memorizing functions and random facts was useless (Hey, didn't Watson just show us this?). What's the point? Won't you have a book in real life? Why not?

I'm of the opinion that math/physics/chemistry tests should be open book. Education should teach you to be able to think and solve problems, not be a walking encyclopedia. That way you can make TOUGHER questions where the student has to recognize the elements of the problems and put it all together t

I honestly don't understand the attraction for totally closed book exams.

Back when I was teaching Chem101, I let my students bring in a 3x5 card with any formulas or notes they wanted. The final got an 8x11 sheet of paper. This solves a couple of issues- it massively reduces cheating since you're allowed (some) notes, and it forces the student to figure out what's on the card, since space is limited. Anyone who spends the time figuring that out has just done a whole pile of studying without realizing i

In fact it was open book, open note, open teacher. You could go ask the teacher for help. He wouldn't give you the answer, but he'd help steer you on the right course. I learned more in that class than in any other. Now of course people are quick to say "No you didn't, you just liked it because it was easy." Actually it was not easy, but my appreciation for how much I'd learned came not from that class, but after.

So first thing to understand is that I'm good at math, but not stellar. I was never the stereotypical "Better than everyone at math and loving it," geek. I did well, got to advanced (but not advanced placement) math classes, usually got Bs and As and so on, but I was no super math whiz, and while I didn't hate it, I didn't really like it that much.

It was a precalc class, taken my senior year of high school. So in university I started in Calc 1 as you'd expect. At the beginning of the second class, the teacher gave us a precalc test. It was to be fully graded, though not counted. He said he was doing this first to get a feeling for how much precalc he needed to cover since it often got taught wrong, and also to help people who might not be ready for Calc 1. If you bombed the test he didn't kick you out, but suggested that you might wish to transfer to precalc since it was unlikely you'd do well.

I just aced that test, near 100%, by far the highest score in the class. He came up and asked me where Id' learned precalc, since it was so rare to find someone with such a solid knowledge of it.

Never before or since had I learned so much in a math class, and he allowed calculators, the book, any notes, and asking him questions. The tests were about learning how to do the math, how it worked, not about making sure you could do the fiddly stuff in your head.

As a mathematics teacher I always encouraged my students to show working as a means of giving them partial marks for partially correct answers.
Very hard to award marks for working out that is not there even if I can see what they *probably* did wrong to get the mark they did.

Personally, I think as far as math education should go, the more crippled, the better. The most advanced calculators make kids dependent on them when learning. Let's let them use calculators that can only give them the most basic info like a replacement for Trig tables or for basic calculation. Anything more and the kids will learn more about the calculator and less about the subject.

Personally, I think as far as math education should go, the more crippled, the better. The most advanced calculators make kids dependent on them when learning. Let's let them use calculators that can only give them the most basic info like a replacement for Trig tables or for basic calculation. Anything more and the kids will learn more about the calculator and less about the subject.

Except you get out in the real world and the last thing you want is your engineer pulling formulae from their (faulty) memory when they are already available in the computers they will be using. Maybe we should teach people to do things the way we actually do things in real life. Nobody teaches doing basic arithmetic with a piece of charcoal on the back of a shovel any more.

Then maybe math should become less about solving formulae and more about identifying variables and constructing formulae to obtain the needed information. It's not a bad idea by any stretch, though how workable it is could be debated.

It has been my experience that most word problems in school settings are HIGHLY contrived, and are basically just restating the desired formula in sentence form.

More useful for the engineering student would be to pose a problem, rather than to ask a question. EG:

Create a formula for a 3D lofted surface that produces the maximum lift with the least drag for an object 10 meters long and 5 meters wide. Due to material fragility, max strain cannot exceed 30ka/cm^2, and wind sheer restricts max airspeed to 120kp

If you don't need to do anything then you don't need to know anything.If they are going to grow up to just follow standard operating procedures devised by somebody else then go home and watch TV they may never need that stuff. If they are going to do a bit more or have hobbies that involve working with physical objects then they might need that stuff.I was lucky and grew up reading Martin Garner's Mathematical Puzzles and Diversions column in Scientific American which helped make it interesting and connec

Knowing what formula, what it means, what assumptions it requires, and what limitations it has, is key. That means memorizing its details.

Simply programming the solution into your calculator doesn't teach you anything but what the formula is. It doesn't demonstrate any knowledge of when/why/how to use the formula.

It's the same level of knowledge that has a student saying the answer to a problem is "1" when he uses an RPN calculator. He had the formula written down in front of him, but wasn't smart enough to realize the vastly wrong answer when he thought he was using it correctly. (He pressed an additional ENTER and wound up dividing one number by itself.) This problem dealt with the concentration of hydrogen ions in a buffer solution, and it should have been obvious that '1' was a completely ridiculous answer. (The real answer was around 10e-6.)

Except you get out in the real world and the last thing you want is your engineer pulling formulae from their (faulty) memory when they are already available in the computers they will be using.

No, the last thing you want is your engineer picking an equation to use because it looks like it might apply and it has been programmed into the computer for him. The correct problem solving method means knowing the problem to be solved first and then solving it, not picking from a list of problems that have already been solved and reproducing it.

Calling these calculators "crippled" is wrong. They are limited in function, deliberately. (car analogy) It is like calling a VW bug "crippled" because it isn't doing the job of a 1/4 ton pickup truck. (/car analogy).

They are smaller, cheaper and lighter than a computer (even a netbook, and much cheaper than an iPad). They are harder to use to cheat, and unfortunately, that is an issue that makes them better for classwork than those full computers with fancy software. They are just the right level to remove the tedium of doing basic math (which should have been mastered by now) while leaving the requirement to think through the problem to know what basic math needs to be applied.

I've always had the philosophy that you should take it one further and skip calculators altogether in math class. For harder K-12 math, there's no real calculations involved, just express your answer without evaluating the actual value of the square root of 5 or pi or sin(3), etc. Students shouldn't need any help doing basic arithmetic. Which is why they shouldn't need calculators for easier math either (if they need them, they deserve to fail). For classes in physics or chemistry, basic calculators should

Thing is, if they're being bought primarily for the lack of features, it seems hardly worth bothering with an expensive graphing calculator in the first place. If you don't want people using equation solvers, storage capabilities, and so forth then they're pretty much a total waste of money (and if you need to do these things in real life, that money is better spent on a copy of Mathematica). I bought one in school, just like everyone else on the course, and I don't think I ever actually used any features you wouldn't find on a $10 scientific calculator.

If I need to plot a graph, or get the roots of a difficult equation, or whatever else, I'll do it on the computer. If I'm in an exam designed to test my ability to do those things, it'll probably be written in such a way that the calculator can't just do it for me. The overlap between things that can be tested in an exam, and things that a graphical calculator can do but a scientific calculator can't, is minuscule, and really doesn't seem worth making everyone buy the things just to test that tiny area.

When I was in high school not that long ago, the graphing calculator was an integral part of the calculus curriculum. Back in '96, even the cheapest desktops were often beyond the pocketbook of my classmates, to say nothing of net/notebooks. I am unsure of the current pedagogic inclinations in math education, but others seem to be chiming in on this thread and at least a few are saying it is still important in the classroom. Beyond high school, however, my personal experience has been that HP graphic cal

I think modern technology should be integrated with learning. I don't think of it as a crutch just like an abacus isn't or a calculator isn't. It's a tool that previous generations invented for the betterment of society and we should use them.

Cause the large portion of students are untrustable cheating bastards?

"Cheating" is a concept that only makes sense in the context of "testing". In the real world, cheating would be called "collaboration".

We have a system of education designed around preparing people for solitary, boring, mindless work.

If you're good at working by yourself on predictable problems you will do really good at high school (and pretty well at college) in the US. If you thrive when interacting with other people and coordinating amongst a variety of skills to solve difficult problems, that ability

You're clearly expecting the best of people (that's ok - I do too, and I'm happily justified in doing so much of the time. However...). In the *real* real world, this "collaboration" you refer to often boils down to this: the folks that cheated their way through their educations ride on the backs of those who didn't. The former can't actually do the work their jobs require (or at least not at an expert level), so they rely on the latter to carry the load. A team context makes it easier for such people

Why, yes indeed. I worked in industry for many years, and I can tell you that no workers were more highly valued than those who were unable to do even the simplest things by themselves. "Let's collaborate!" they would say, and our hearts warmed instantly and we leapt into action, "helping" our valued coworkers, doing their work for them. In contrast, those with highly valuable skillsets, able to quickly solve difficult problems, those were as dirt to us. "Be off with you!" we'd cry, "and never dare to cross our path again!" Yes, as sweatyboatman says, nothing is more valuable in the real world than incompetence!

In fact, if you work for any sort of business with more than 5 employees, you've been doing exactly that!

Except you apparently failed to note that the workers who call for "collaboration" have positions and titles like: managers, bosses, CEOs etc. It is exceptional indeed if any of them is capable of doing even a fraction of actual work his or her underlings do since they've, quite successfully may I add, invested all their time into skills to induce "collaboration" with others in which they reap nearly all the benefits.

And, surprisingly, a vast majority of those with "valuable skill sets" waste no time in their rush to "collaborate" with the said individuals, likely including you. It is only your fellow competitors for the favors of these masters of yours, or people whom you intend to "collaborate" into your own personal gain, that you reserve all your disdain for: those better know what they are all about, lest no profit!

As it is, in the "real world", "cheating" is one of the most valuable skills in our duplicity-based society: that is how the social elites are made. Those who learned early on to "play by the rules" are doomed to be forever serfs and to "collaborate" for those who did not.

Honestly, the real reason for the demand for crippled technology is the idiocy and cluelessness of high school maths teachers. What's the problem with writing a TI-BASIC program to solve a formula?

When I was in high school (the mid-late 90's), the first thing I did when I understood a formula was to write a program on my calculator to solve it. (I did the same thing on my Debian box at home, but in C, just to make sure I wasn't being retardedized by BASIC). This was before the days of 'wipe your calculator

Today I'm a programmer, and I make more than twice what my idiot math teachers made, and probably have more fun doing it.

As a programmer, you must have experience with the following phenomenon: you come back to a piece of code you yourself wrote, a year or so later, and not only can you not remember how it works, you don't even remember that you're the one who wrote it. It's great and everything that you could turn the formulas into a computer program, but as a fellow programmer myself, I can tell you that I can turn all kinds of formulas into programs even if I don't understand the damn formulas.

The goal, which you apparently missed completely, was to learn math, not how to turn a formula into a computer program. There's simply no way around the fact that most of this stuff can only be mentally internalized by rote and repetition. It sucks, it's boring, it's also how learning happens. What you did, and your following smart-ass attempts to defend your case, had a quite foreseeable outcome. Although I commend your mother for going to bat for you. Seems like parents don't have the guts for that in most cases lately.

I completed a BSc. Electrical Engineering degree - 8, I think mathematics courses - without using a single calculator in an exam. The mathematics department, quite rightly, forbade their use. They have no part in a mathematics exam, as does any exam that requires you to use a calculator. Why not just substiute x and use values that cancel out, or work out nicely? It has the benefit of helping you know you've done something gravely stupid.

Calculators, and use of symbolic integration and other packages were o

A corollary in support of your point: the ability to manually work through the basics of math are essential if only because the reliance on more and more complex systems REQUIRES that the humans doing so have some 'common sense' ability to interpret the results, and double check them in a basic sense.

True story: I bought something for a few bucks. I handed the teller a $10. She punches it into the register, and hands be $14 back in change. Patently impossible. So I said "I'm not sure this is my right ch

because Texas Instruments has lobbied very successfully to keep it that way.

Precisely WHO would TI lobby?

Not sure, but I was required to purchase a specific TI calculator for my kid just about four years ago, for a public high school trig class. If you didn't, you could fill out the forms with giving evidence as to why you couldn't afford it, or your child could take a less rigorous class. Great system, I wonder who gets paid off.

The only point I ever saw for them was the coolness factor. That was back in the 1980s, though.

Cool was having a top-of-the-line log-log slide rule with leather case. I had a Pickett 500 until some asshole stole it out of the biochem lab. Then I moved up to a
to K+E log-log decitrig. That was back in the 1960s, though. Get off my lawn.

The only point I ever saw for them was the coolness factor. That was back in the 1980s, though. With today's tech, a dedicated calculator seems... at best, quaint.

OK, as the publisher of an iPhone calculator (Perpenso Calc [perpenso.com] RPN, 5 modes: Scientific Stats Business Hex Bill) I may be biased, but apps will eventually displace handhelds. It is just part of digital convergence, we will ultimately only be carrying around a single pocket sized electronic device.

Regarding web access during tests, things like "airplane mode" where all the wireless circuitry is disabled will do. It will take time for teachers/professors to catch up but a few years ago I had professors who we

They're small enough to be pocket portable ( smart phones could handle that , but awkward to type on to meMy ti-83 lasts forever on a battery set of easily replaced AA'swhile it's not impossible to cheat; it is a lot harder to slip in hidden notes in a calculator.

Why are we having exams that require a calculator?I did all of calculus and most of linear so far(sufficiently complex equations were done to allow for matlab use, but the test stuff could be done without), and even statistics(yay longhand division!) without one just fine, and most problems can easily be done without them if the proper setup numbers are used.

Also, they are NOT crippled enough. Even when i was in middle school there were program packs to download your textbook onto your ti-83 (I had a ti-80 and i could still type the formulas by hand) so they are still too advanced to not cheat with. And don't tell me you can just wipe the memory, any sufficiently smart cheater would have a ti with a different spare battery. You can find easy DIY's for those online nowadays easy.

Allow a calculator with a 10 key, if they need to graph something, then they should be able to figure it out enough by hand and not need a calculator.

All testing with a graphing calculator does is let more students pass because they don't need to learn, they just need to throw thier notes on the calculator memory. (Yes you'd have references in real life, but the point of most math tests is it's so basic you shouldn't NEED references, it should be the core material you know by heart)

I agree that you shouldn't "need" a calculator, but on a test in a non-math class, it's nice to have. For instance, in Physics, maybe you have a bunch of problems involving kinematic equations and you barely have enough time to set them up. It's nice to be able to use the calculator to reduce your augmented matrix into RREF. Sure, I can do it by hand, but I don't always have time on a test. With a TI-89, I can save a bunch of time by taking the grunt work out of the equation. And a laptop wouldn't work because what kind of teacher is going to let students have internet access during a test? (not to mention access to scanned copies of their notes, etc.)

I have to disagree with this. When you go on to actually use the math you've learned, not using a calculator is plain silly. There is no way I could have completed a few EE exams without my TI89 because of the large amount of complex (in both uses of the term) math required. I remember a number of my friends had trouble simply because they didn't know how to use their calculators and had to do their calcs by hand. I'm sorry, but when you have a test with a dozen problems, each requiring as much number crunching as an average calc exam, you need the calculator.

And now that I'm all grown up, I'm not going to model a filter by hand on a piece of graph paper. I'm going to use Matlab. If an engineer wanted to do math by hand today, they'd be seen as a dinosaur wasting time - not some mathematical genius.

If you really want to prepare people to use math in the real world, you need to include teaching them how to use today's tools. Teaching students how to do things by hand is great, but utterly useless by itself after they complete the final.

If you can do the math without the calculator you can almost certainly do the math with the calculator. However you cannot say the same about the situation where you learn and practice using a calculator. A common stumbling block for students is when you take nearly all the numbers out and ask them to solve it. A lot of students can't identify if they've got the correct answer without checking against the calculator.

If you really want to prepare people to use math in the real world, you need to include teaching them how to use today's tools. Teaching students how to do things by hand is great, but utterly useless by itself after they complete the final.

You are giving the same bogus "it saves time" argument as above, but then you give an even worse one. No, mathematics shouldn't teaching pure thinking, it should prepare you for the real world.

Maths prepares you for the real world by giving you basic skills you can use everywhere. But you will have to apply them yourself. Making mathematics classes a trade school class as you are suggesting is a travesty. This is similar to crap courses at university where you learn to use some fashionable programming l

There is a generation of scientisits that doesnt know how to use anything but themI used to work in a company, with scientists aged 45 and above, they had linux clusters, powerful desktops with the latest software, but in the office, there HAS TO BE a scientific calculator lying on the desk somewhere.Companies realize that there is still a minor need, and produces for that need accordingly.But i assume that this will disappear.

Because the schools get kickbacks from the book publishers. And the book publishers only publish math books that can be used with specific graphing calculators. Guess who pays off the publishers to do that?

To further the greed, even if they aren't getting kickbacks to increase sales of one line of calculators, they have no incentive to keep up with the tech and rewrite the books.Once they write one book, all they have to do to newer editions is charge the order that the problems are printed in. So its the same book, but different enough to force people to buy the new edition.

One argument heard for using these calculators is: 'They are limited enough to use in exams.' Sounds sensible, but it raises the question: 'Why are we teaching a generation of students to use crippled technology?'"

Do you really want students to have internet access during a test? I know how to solve a system of equations by hand (by reducing a matrix into RREF) but my Physics teacher and Mechanics teacher both lets us use a calculator to solve them on a test to save time. Are you saying they should let me

"...'They are limited enough to use in exams.' Sounds sensible, but it raises the question: 'Why are we teaching a generation of students to use crippled technology?'"

Crippled technology? Hell, why do we even allow calculators to be used in ANY exam? What's the point in "teaching" math if you let the calculator do 90% of the work? And no, I'm not talking about "show your work" when solving for seriously complex calculations, I'm talking about what 95% of high school students are "taught" and yet the system allows them to pass through with flying colors due to massive hardware "grants" from Texas Instruments.

In the calculus classes at my school, calculators were not required, but their use was encouraged as a learning tool... except during exams, where they were forbidden.

To me the policy was analogous to that of the organic chemistry classes, where homework counted almost nothing toward your grade and in some cases wasn't collected at all. If you never turned in any homework, it wouldn't hurt your grade... but if you thought you were going to pass the exams without doing the work, you were in for a rude awak

What's the point in "teaching" math if you let the calculator do 90% of the work?

What's the point in "teaching" math if you let the decimal system and all that clever carry-the-one shit do all the work? I mean seriously, students need to learn what addition really is -- make them put 198 beans into a pot, then put another 61 beans in the pot, then count the beans to get the answer.

Being a human is about being smart, not being dumb. Forcing a student to do addition on paper when the student is studying partial differential equations is nothing but an insult. By that point I think they've earned the right to not continually have to prove that they can add two numbers together.

As an undergrad taking physics I had this bad habit of forgetting my calculator, especially on test day. I'd end up doing longhand division and taking up half the paper and leaving less room to write the actual answer. The professor started asking me what the hell I was smoking.

What's the point in "teaching" wood shop, if you let a power drill do 90% of the work when drilling holes?

Students should have to do it using hand screws, lest they become dependant on the newfangled lctricity!!

Crippled technology? Hell, why do we even allow calculators to be used in ANY exam? What's the point in "teaching" math if you let the calculator do 90% of the work?

Because calculators are a tool used by practitioners of mathematics, and students benefit from learning to use the tool to facilitate their work?
Because arithmetic is simple, and it would be wasteful to just be constantly re-testing all that particular type of "work" on every test?

Don't take testing of students' ability to use a calculator for granted.... many students fail, even with advanced calculators fully allowed.
To be successful in life, you have to learn how to use a calculator, and if math classes don't teach this and test you on it, many students won't get the required skill.

It turns out that in real math classes you actually have to have some idea what you are doing to be successful even with a calculator.
This couldn't be more true than with word problems that sometimes involve many steps and pages of work, and require advanced problem
solving --- the more work the calculator can do, the more time the student has to do work on the real math (problem solving), AND, therefore
the more complex the problem can be, and the larger the amount of material that can be tested (the more advanced the thought that can be required of the student).

In other words use of a calculator is not harmful, and actually beneficial, if the examination method is effective, and accounts for the students' access to a calculator. Strategy for using the calculator in an appropriate way is also a problem solving consideration -- if the student uses their calculator inefficiently, or doesn't take a good problem solving approach, they will run out of time before they finish the exam.
The introduction of this strategy element allows the exam to be made more challenging, and therefore....
taking the exam more rewarding / more educational an experience.

If you can't use a calculator, you won't go very far in modern maths. If you can use a calculator, 98% of the students will have their needs met;
the 2% who go into advanced maths for maths sake are such geeks they will not be harmed by learning to use a calculator.

This same topic seems to get re-submitted to Slashdot about twice a year.

Short answer: If you need 100MB for a calculator, I salute you. If 320*240 pixels with 65,536 colours is too small and low-res for you for a calculator, you should save your money for a trip to the eye doctor.

Can a netbook do more different things than a calculator can? Yes, yes it can. That is why a calculator is not called something else... like, say, a netcalcubooklator.

My cell phone lets me make phone calls and also play Angry Birds. Why is Uniden still selling phones that don't have built-in synchronization to Google Contacts?

My 24" widescreen LCD monitor can display six pages of a book at once at full resolution. How do Amazon and Barnes & Noble get away with selling devices that can only display one page at a time, are not backlit, and can't run Photoshop?

The answer is obvious: There is plenty of room in the world for purpose-built devices. The reasons why people like to use those devices will vary. I, for one, like having a compact calculator that is programmable and has plenty of easy-to-stab dedicated calculator buttons on the front (as opposed to messing around with LaTek formula input, or whatever other input method you'd use on a device with a keyboard or touchscreen). My calculator of choice is an HP 50G. The HP 48 emulator on my Android phone can do most of what the 50G can do (and probably a lot faster), but as an emulated calculator on a touchscreen device, it ain't the same.

Do I use my programmable calculator every day? No, no I do not. Do I resent spending $120 on a calculator, compared to the cost of the chemistry textbook I bought for the same class? No, no I do not.

If a low-end netbook cost 5 times as much as a graphing calculator instead of twice as much, we wouldn't be asking this question.

If it weren't for virtual "vendor lock in" dictated by testing agencies, book publishers, and other "high influence" players giving TI a near-monopoly, the price of these fancy not-a-computer graphing calculators would be more like $25-$50 instead of $80-$130. Oh, and netbooks wou

Just too bad that HP decided to stop making the 15C, it has a great format, is competent and is easy to use. A modern version with more memory, a micro SD card slot and a faster processor would be sufficient. No reason to add any additional math functions.

Seems to me a similar story was posted not too long ago. Summary of the discussion: graphical calculators serve as an anti-cheating tool, as they cannot be programmed, except that they can be programmed if you're smart enough, and therefore actually serve no purpose. The only practical solution seemed to be providing students with a school owned graphic calculator at the beginning of the test (thus taking away any opportunity to pre-program the calculator).

'Why are we teaching a generation of students to use crippled technology?'"

I was under the assumption that tests weren't about how good you were with technology or how quickly efficiently you could use technology to find/give you the answer, but rather that they were about being able to determine how well a student grasps the concepts, facts, and functions of the matter on which they are being tested. I thought these tests were supposed to be about the student, not about the technology.

I really don't understand why those things are used! The only time I ever "needed" a graphing calculator was in high school. In college, not a single math class allowed calculators, at all. Even the calculus courses! The only thing I ever used my TI-83P for was loading it up with equations (in the notepad app) for physics. And in physics, the hard part is knowing which equation to solve given the problem, not how to do math. Most of the time we were allowed cheat sheets anyways. These things are useless. I

For general use, dedicated calculators have gone the way of dedicated mp3 players or feaure phones. I have an HP emulator on my iPhone as well as Wolfram!Alpha. Unless on loves he keyboard, which is not all ha easy o use, these to applications take the place of my huge HP 49 or TI-89 or whatever.

That said one can't use a smarphone on a test. That is why over the past 10 years calculators have no been designed for he professional, but for the testing companies. Pro features are removed to make it acceptable for the standardized test. Ad copy basically focuses on this. I believe the TI nspire even has an interchanabled keyboard that limit functionality so it can be used on tests.

I don't see any reason to teach the calculator other than it is a necessary test taking skill. As long as the public gives credence to the AP exam, as long as states believe calculators are more important than basic skills, as long as calculator manufactures pay politicians to require calculators in the classroom, we will have them. OTOH, it is much more likely to get a kid o use a calculator to do work, rather than a computer where they go off and play WOW.

I haven't run any exact tests, but I've gotten a TI-83+ running on solar panels, in full sunlight, rated at 6V, 100 mA (600 mW). I also have an Eee PC 701 that consumes roughly 26 watts of power when it runs directly off the wall charger. I'm not sure how efficient today's netbooks are, but that's a big difference.

I teach physics for a living. Different profs run their courses in different ways, but personally I feel that memorization is evil, so I give open-notes exams. Therefore I don't really care whether students use graphing calculators that can store all their equations for them. To me, the bigger issue is preventing students from accessing internet and cell networks. I don't want them communicating with someone outside the room who will help them on the exam. This is why I let them use a calculator on an exam

One argument heard for using these calculators is: 'They are limited enough to use in exams.' Sounds sensible, but it raises the question: 'Why are we teaching a generation of students to use crippled technology?'"

The real question is - "Why aren't we teaching students to better understand by graphing themselves, rather than relying on a machine?"

Granted, it's a lot easier to use a machine to graph than going through the drudgery of drawing the graphs; but slogging through graphing is part of developing not just an understanding of the process, but a feel for the answer so you can recognize one that isn't right and look for your data entry errors.

I graded papers or engineering classes and would get (wrong) answers to

The real question I think is why are we crippling yet another generation with technology that thinks for them? Kids need to learn how to sketch by hand, and how to compute approximate numerical answers in their heads.

Pocket calculators are responsible for at least two generations of innumerate kids already. Netbooks with math software won't solve that problem in the future. There is no royal road to geometry, calculus, or arithmetic.

My TI-whatever had like 500 bytes of memory, and I could cram so many physics, economics, or statistics formulas into that space. Which begs the question of why I ever had to "memorize" any of that, since now I just look up whatever I need to use.

Teachers are lazy. They expect students to come up with original un-plagiarized answers to test questions the teacher/professor hasn't updated in 20 years and probably copied wholesale from a textbook somewhere. If you really want original answers, come up with some original questions.

For me, it's the fact that it's small, portable, and has a real keyboard.

If I have a bunch of numbers on paper to add up, I grab my HP-15C because I can set it right next to the paper, and I can use the keyboard to type the numbers on it much faster than doing it on my computer and having to look at the screen to compare with what's on the paper.

I have an RPN calculator on my smartphone, but it's not as usable as the calculator without a keyboard.

If I were doing graphics or anything more advanced, then I'd just use my computer. I have an old HP-48 which I never use because it's too complicated for anything non-trivial and for anything trivial, the HP-15C is better. When I bought it, it was great and I even wrote some programs to automate some tasks, but now it's much easier to use a real computer.

A basic scientific calculator should be so cheap these days that they could just be added to the instructors budget and handed out to students and returned to the instructor during a test. I see no reason in this day and age where basic calculators shouldn't be as readily available as say, a pen.